LMS Journal of Computation and Mathematics

Research Article

Non-variational computation of the eigenstates of Dirac operators with radially symmetric potentials

Lyonell Boultona1a2 and Nabile Boussaida3

a1 Ceremade (UMR CNRS 7534) Université Paris-Dauphine, Place de Lattre de Tassigny, F-75775 Paris Cedex 16, France

a2 Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom (email: L.Boulton@hw.ac.uk)

a3 Département de Mathématiques, UFR Sciences et techniques, 16 route de Gray - 25 030, Besançon Cedex, France (email: nabile.boussaid@univ-fcomte.fr)

Abstract

We discuss a novel strategy for computing the eigenvalues and eigenfunctions of the relativistic Dirac operator with a radially symmetric potential. The virtues of this strategy lie in the fact that it avoids completely the phenomenon of spectral pollution and it always provides two-sided estimates for the eigenvalues with explicit error bounds on both eigenvalues and eigenfunctions. We also discuss convergence rates of the method and illustrate our results with various numerical experiments.

(Received November 20 2008)

(Revised March 28 2009)

(Online publication January 2010)

2000 Mathematics Subject Classification

  • 47B36 (primary);
  • 47B39;
  • 81-08 (secondary)